Question: The grades on a language midterm at Springer are normally distributed with $\mu = 70$ and $\sigma = 3.0$. Jessica earned a $69$ on the exam. Find the z-score for Jessica's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Jessica's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{69 - {70}}{{3.0}}} $ ${ z \approx -0.33}$ The z-score is $-0.33$. In other words, Jessica's score was $0.33$ standard deviations below the mean.